In Sect.  we focused on the double-minus amplitude and
derived bounds on the Wilson coefficients along the lines of
Ref. [1]}, [2]}, [3]}. We expressed the
low-energy expansion coefficients as dispersive integrals in
Eq. (REF ). We then identified the two-sided
bounds on the coefficients following the observation in
Ref. [3]} that the boundaries of the allowed
region inherit the cyclicity property from the one channel dispersion
relation. In this way, by explicitly extracting the mixed constraints
from the mixed \(s\) –\(u\)  channel partial waves we identified the new
boundaries of the allowed region. We do not rigorously prove that our
identification of the bounds is optimal, and we leave filling this
gap for future work. We then introduced the idea of LSD which
expresses a relationship between moments of the spectral functions of
various spins, and we used crossing symmetry or null constraints
[2]} to derive rigorous bounds in terms of a few
low-spin partial waves. We found that all the amplitudes considered in
this paper lie on small islands whose location and shape can be
determined using the low-spin dominance principle.
